A tensioning device of this type has been known from the publication DE 198 55 627 A1. Here, through the use of a securing element the tensioning rail can be mounted to and released from a form element connected to the support member. In order to fix the position of the tensioning rail on the support member, the form element engages a recess in the tensioning rail in a form-fitting manner or contacts a side flank of the tensioning rail.